Question: $J$ $K$ $L$ If: $ JL = 92$, $ JK = 5x + 5$, and $ KL = 8x + 9$, Find $KL$.
From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {5x + 5} + {8x + 9} = {92}$ Combine like terms: $ 13x + 14 = {92}$ Subtract $14$ from both sides: $ 13x = 78$ Divide both sides by $13$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $KL$ $ KL = 8({6}) + 9$ Simplify: $ {KL = 48 + 9}$ Simplify to find ${KL}$ : $ {KL = 57}$